Triple centurion Brook happy to break his dad's club record
The 25-year-old smashed a career best 317 that, coupled with Joe Root's 262, helped visitors pile 823-7 declared - fourth highest total in all Test cricket - England's third best.
With a big 267-run lead over Pakistan in the first innings, England then caught the home team napping at 152-6. At close, Pakistan still needed 115 to avoid an innings defeat on the final day Friday.
Brook said his father's highest score was the target.
"I just wanted to get past my dad's high score 210," said Brook of his father David's score in a club match for Burnley in 2001.
Brook had missed a chance of surpassing dad's best when he scored 186 against New Zealand at Wellington last year.
"I said that to you guys before," he said. "I was pretty happy when I got past his score, to be honest."
Brook said he was satisfied to contribute in team's strong position.
"I am lost for words, to be honest," he said. "I'm just happy that the team's in a strong position to win the game tomorrow morning. It's an incredible thing."
Brook and Root enjoyed a run feast on a flat Multan stadium pitch, adding a big 454 for the fourth wicket, England's highest partnership in Tests.
It eclipsed the 411-run fourth-wicket partnership by Peter May and Colin Cowdrey against the West Indies at Birmingham in 1957.
"It was wonderful batting with Rooty," said Brook. "We spoke about the game moving forward and going out there after lunch to try and put the foot down and get a decent lead."
"It makes you feel so comfortable when you're watching him at the other end, he makes the game look so easy, and he's playing the ball so late and making the balls look slow."
Brook completed his triple century with a boundary off part-timer Saim Ayub, reaching the mark off 310 balls before he top-edged a sweep off the same bowler and was caught by Shan Masood.
Brook cracked 29 fours and three sixes in his 439-minute stay at the crease. It was Brook's sixth Test century and his fourth against Pakistan following his three in as many Tests when England routed Pakistan 3-0 in 2022.